Contest Duration: ~ (local time) (100 minutes) Back to Home
B - Sum of Three Integers /

Time Limit: 2 sec / Memory Limit: 256 MB

Score : 200 points

### Problem Statement

You are given two integers K and S.
Three variable X, Y and Z takes integer values satisfying 0≤X,Y,Z≤K.
How many different assignments of values to X, Y and Z are there such that X + Y + Z = S?

### Constraints

• 2≤K≤2500
• 0≤S≤3K
• K and S are integers.

### Input

The input is given from Standard Input in the following format:

K S


### Output

Print the number of the triples of X, Y and Z that satisfy the condition.

### Sample Input 1

2 2


### Sample Output 1

6


There are six triples of X, Y and Z that satisfy the condition:

• X = 0, Y = 0, Z = 2
• X = 0, Y = 2, Z = 0
• X = 2, Y = 0, Z = 0
• X = 0, Y = 1, Z = 1
• X = 1, Y = 0, Z = 1
• X = 1, Y = 1, Z = 0

### Sample Input 2

5 15


### Sample Output 2

1


The maximum value of X + Y + Z is 15, achieved by one triple of X, Y and Z.

### 問題文

2 つの整数 K,S が与えられます。
3 つの変数 X,Y,Z があり、0≦X,Y,Z≦K を満たす整数の値を取ります。
X + Y + Z = S を満たす X,Y,Z への値の割り当ては何通りありますか。

• 2≦K≦2500
• 0≦S≦3K
• K,S は整数である。

### 入力

K S


### 入力例 1

2 2


### 出力例 1

6


• X = 0, Y = 0, Z = 2
• X = 0, Y = 2, Z = 0
• X = 2, Y = 0, Z = 0
• X = 0, Y = 1, Z = 1
• X = 1, Y = 0, Z = 1
• X = 1, Y = 1, Z = 0

### 入力例 2

5 15


### 出力例 2

1


X + Y + Z の最大値は 15 であり、それを満たす組は 1 通りです。